The present invention relates to an on-line numerical geometry evaluation method for computation of the particulars standard geometric elements or for complete gauging of the work pieces or parts of work pieces composed of several standard geometrical elements such as cylinders, planes, spheres, cones or torus, combined with or connected to one another with free orientation in the 3-dimensional space, within of all required tolerance conditions according to standards ISO 1101 [1] and ISO 2692 [2] (and beyond of that standard—with tolerances in the elliptically range), such as form, distance, inclination and so on, whereby the measuring points can be given in the Cartesian, spherical, cylindrical or any other coordinate system for which the number of the measuring points is much larger than that of the searched parameters.
The direct application of Chebyshev method is not satisfactory enough in the case of some CMM measurements. This problem is present on non-precise parts of work pieces and in measurements with scanning robots or coordinate measuring machines with lower accuracy.
An another problem is evident during the measurement of the plastic work pieces or measurements on CMM controlled by hand. There are the geometrical deviations present in such a manner, that the Chebyshev method is limited applicable.
By scanning machines controlled by hand beside the well-known effects, acceleration forces and inaccuracies caused by bending, torsion etc., the still following effects are to be considered to,                the forces, which are caused by the operator (with linear and rotary motion with different speeds and forces still combined in different directions)        radial clearance in many bearings        impact and movement without jerking        acceleration forces including impulse and wind up.        
Overlaid deformations of the mechanism caused with all these different forces and moments in different directions, inclusive the hysteresis with some inductive measuring heads by fast change of the direction and size of the forces is caused, can together impair the accuracy such of a robot or a similar measuring machine in such a manner, that despite all corrections measuring errors cause a measurement inaccuracy more largely than 10 micrometers. A conventional direct evaluation according to Chebyshev or the form examination are thus hardly possible. The repetition accuracy with same operator of the measuring machine cannot never be given.
The constant corrections, in particular the bracket and bending corrections of the measuring points as well as constant transformations and inverse transformations of the measuring points during the evaluation, place an additional degradation of the results of measurement.
Many errors, which are caused by hardware, change the true form of the measured surface, with the consequence that to many points of the “filtering criteria” become trapped. As remedial measures fast different filtering were found.
By an method for integrally evaluation of the work pieces, it is foreseen to apply the evaluating principles only either as the integral sum of least squares (Gauss) of all elements (of the body), or as the integral Chebyshev solution (minimum the largest distance between measuring points to the geometric elements respectively of the body). This method is very stable if only least squares (Gauss) method is applied. With the Chebyshev method and by using in the measuring robots or similar measuring machines by non-precise measurement, the same difficulties are present as are described above.
Furthermore in that method are beside a circular form still the squarely and symmetric tolerance ranges foreseen.
The squarely tolerance range form permits that the maximum deviation, which lies in the diagonal such of a square is, larger than everyone of the two regarded tolerance (sides of a square), see FIG. 9.
The non-symmetrical tolerance fields are however required and are very frequent into the tolerating. The elliptical tolerance are very rarely requested in the opposite, although only they can guarantee a perfect maximum allowable deviation.